As long as the motherboard has any sized PCIe slot (1x - 16x) you can purchse PCIe risers like this: https://www.amazon.com/PCI-E-Powered-Riser-Adapter-Extension/dp/B06XHVTCRF/ref=sr_1_6?s=electronics&ie=UTF8&qid=1495766268&sr=1-6&keywords=pcie+riser and just plug the riser into the motherboard and the card into the riser. Mining doesn't use that much slot bandwidth so mining performance is unaffected on the bus speed.

I'm currently using a mobo with 3 16x slots and 3 1x slots and using those risers in all the slots to be able to use 6 cards.

Since you already have an AX1500i you could just buy more cards or use those 470s and the 1060 and the risers and plug them into any open PCIe slot on your motherboard but you might have to do some research to see if your motherboard can hold 4-5+ GPUs.